\chapter{Introduction}
\begin{flushright}{\slshape    
Every river appears to consist of a main trunk, fed from a variety
of branches, each running in a valley proportional to its size,
and all of them together forming a system of vallies,
communicating with one another, and having such a nice adjustment
of their declivities that none of them join the principal valley
on too high or too low a level} \\ \medskip ---
\citeauthor{playfair:1802}. \citetitle{playfair:1802},
\citeyear{playfair:1802}
\end{flushright} 

Landscape evolution is one of the main topics geomorphological
science deals with. It can be defined as a continuous process
resulting from \blockcquote[see][p. 247]{pazzaglia:2003}{the
interactions between form and process that are played out as
measurable changes in landscapes over geologic as well as human
time scales}.
Among the processes which affect landscape evolution, river
networks development assumes a relevant role.
In fact, water and sediment interactions shape hillslopes,
regulate soil erosion and sedimentation, and organize river
networks, iteratively.
Since landscape evolution and river organization occur at various
spatial and temporal scale, involving a great amount of factors
and drivers, the understanding and modeling of them is highly
complex.

Many modeling approaches can be found in the pertinent literature.
Among them, the idea of a least action principle governing river
networks evolution has been proposed many times as a simpler
approach than a physically based one when applied at the basin
scale.
This theory assumes that river networks, as observed in nature,
self-organize and act on soil transportation in order to satisfy
the \enquote{optimality} criterion of least energy expenditure.

Yet, since its mathematical formulation implies too many degrees of 
freedom if compared to the available equations, the problem cannot 
be solved easilly. For this reason, various
simplifications, like 2D analisys or single section focus, have
been proposed by different authors.
The simplifications depend on which time and spatial 
scale we are focusing on, and then on the type of framework we are 
interested in, \ie for system understanding or modeling for management. 
Thanks to \acp{DEM} and increased computational power, it is now possible
to study the 3D structure of river networks. For this purpose the
suggested simplifications fail to characterize both the whole
complexity of river networks branching and longitudinal bed
profiles.

Considering this statement, the following questions rise:
\begin{itemize}
  \item May the principle be used to represent the landscape
  evolution process in time and space process using \aclp{DEM}?
  \item Would a multi-objective framework be suitable to take
  advantage of the existing knowledge and to assess the tradeoffs
  among different simplified version of the \enquote{optimality}
  criterion in order to find the proper expression for 3D
  modeling?
\end{itemize}
The main objective of this thesis is to give an answer to these
questions.
In the attempt to pursue this objective, we detailed a
multi-criteria optimization framework to describe river and
landscape evolution in a 3D spatial domain.
It is composed by:
\begin{itemize} 
  \item a model which, given a discretized landscape \ie a
  \ac{DEM}, builds the relative river network and evaluates the
  value of the criteria.
  For building the algorithm of the model, the main features of a
  \ac{GLE} model, developed by Professor Kyungrock Paik from Korea
  University were taken as a basis, re-elaborated and
  improved;\footnote{For a description of Professor Paik's \ac{GLE}
  model, see \cite{paik:2011}.}
  \item an optimizer which generates synthetic landscapes,
  exploiting evolutionary algorithms, and, coupled to the model,
  performs the optimization of multiple objectives;
  \item a set of analysis tools and methods for assessing the
  features of the synthetic landscapes, generated by the model.
\end{itemize}

The joint analysis of multiple objectives might help the
identification of the real optimality principle and foster the
debate around the theory of optimality in landscape evolution
processes.
Furthermore, the framework is expected to point out which
limitations are due to modeling flaws and which instead depends
on the criteria considered.

\section{The contents of this thesis}
The mentioned topics will be debated in the next chapters of this
thesis, according to the following structure:
\begin{itemize}
  \item \MyChap{chap:landscapeEvolution} provides the basic
  theoretical knowledge about the topic of landscape evolution
  under river dynamics.
  After that, the deliverable contribution of this thesis, \ie the
  multi-objective framework, is introduced;
  \item the framework is formalized with mathematical terms in
  \myChap{chap:testingOptimality}.
  Moreover, all its features and the way it works are
  characterized, together with its outputs and the methodology for
  analyzing them;
  \item in \myChap{chap:instanceOfFramework} the elements of the
  framework described in the previous chapter are detailed from
  the technical point of view of implementation.
  Input parameters, model settings, algorithm technicalities both
  for the model and the results analysis tools are deepened.
  \item Finally, the main simulation results are presented and
  analyzed in \myChap{chap:simAndFindings}, describing the model
  setting used for generating them, the main findings and the
  criticalities.
  After that, the fore is left to a short conclusion, with final
  remarks and suggestions for future research.
\end{itemize}

